Universal Hole-Filling Strategies for Coprime Arrays

Coprime arrays (CAs) are found to be captivating for striking a balance among the increased number of degrees of freedom (DOFs), reduced mutual coupling and applicable aperture. However, holes in the difference co-array (DCA) reduce the achievable number of DOFs, and further restrict the complete utilization of the aperture. In this paper, we propose novel universal hole-filling strategies to construct hole-free DCAs. We present universal configuration expressions for extant CAs and derive generalized symmetric relations between holes and inconsecutive lags in DCAs along with their explicit numbers. Based on the universal expressions and the symmetric relations, we propose universal hole-filling strategies by incorporating an additional sub-array outside the original CAs. These strategies that effectively accommodate existing CAs generate hole-free CAs with double-time number of DOFs compared with the original CAs. Finally, we provide numerical simulations to demonstrate that the modified CAs using the proposed strategies precede the original types in terms of DOFs, performance of direction-of-arrival (DOA) estimation and spatial resolution.